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Asymptotic Approximations of Ratio Moments Based on Dependent Sequences

Author

Listed:
  • Hongyan Fang

    (School of Mathematical Sciences, Anhui University, Hefei 230601, China)

  • Saisai Ding

    (School of Mathematical Sciences, Anhui University, Hefei 230601, China)

  • Xiaoqin Li

    (School of Mathematical Sciences, Anhui University, Hefei 230601, China)

  • Wenzhi Yang

    (School of Mathematical Sciences, Anhui University, Hefei 230601, China)

Abstract

The widely orthant dependent (WOD) sequences are very weak dependent sequences of random variables. For the weighted sums of non-negative m -WOD random variables, we provide asymptotic expressions for their appropriate inverse moments which are easy to calculate. As applications, we also obtain asymptotic expressions for the moments of random ratios. It is pointed out that our random ratios can include some models such as change-point detection. Last, some simulations are illustrated to test our results.

Suggested Citation

  • Hongyan Fang & Saisai Ding & Xiaoqin Li & Wenzhi Yang, 2020. "Asymptotic Approximations of Ratio Moments Based on Dependent Sequences," Mathematics, MDPI, vol. 8(3), pages 1-18, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:361-:d:329554
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    References listed on IDEAS

    as
    1. Garcia, Nancy Lopes & Palacios, José Luis, 2001. "On inverse moments of nonnegative random variables," Statistics & Probability Letters, Elsevier, vol. 53(3), pages 235-239, June.
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    3. Wenzhi Yang & Shuhe Hu & Xuejun Wang, 2017. "On the asymptotic approximation of inverse moment for non negative random variables," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(16), pages 7787-7797, August.
    4. Xuejun Wang & Chen Xu & Tien-Chung Hu & Andrei Volodin & Shuhe Hu, 2014. "On complete convergence for widely orthant-dependent random variables and its applications in nonparametric regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 607-629, September.
    5. Wang, Xuejun & Hu, Shuhe & Yang, Wenzhi & Ling, Nengxiang, 2010. "Exponential inequalities and inverse moment for NOD sequence," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 452-461, March.
    6. Wenzhi Yang & Zhangrui Zhao & Xinghui Wang & Shuhe Hu, 2017. "The large deviation results for the nonlinear regression model with dependent errors," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(2), pages 261-283, June.
    7. Kaiyong Wang & Yuebao Wang & Qingwu Gao, 2013. "Uniform Asymptotics for the Finite-Time Ruin Probability of a Dependent Risk Model with a Constant Interest Rate," Methodology and Computing in Applied Probability, Springer, vol. 15(1), pages 109-124, March.
    8. Shuhe Hu & Xinghui Wang & Wenzhi Yang & Xuejun Wang, 2014. "A Note on the Inverse Moment for the Non Negative Random Variables," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(8), pages 1750-1757, April.
    9. Xuejun Wang & Yi Wu & Shuhe Hu, 2016. "Exponential probability inequality for $$m$$ m -END random variables and its applications," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(2), pages 127-147, February.
    10. Wu, Tiee-Jian & Shi, Xiaoping & Miao, Baiqi, 2009. "Asymptotic approximation of inverse moments of nonnegative random variables," Statistics & Probability Letters, Elsevier, vol. 79(11), pages 1366-1371, June.
    11. Aiting Shen & Yu Zhang & Benqiong Xiao & Andrei Volodin, 2017. "Moment inequalities for m-negatively associated random variables and their applications," Statistical Papers, Springer, vol. 58(3), pages 911-928, September.
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    Cited by:

    1. Michal Pešta, 2021. "Changepoint in Error-Prone Relations," Mathematics, MDPI, vol. 9(1), pages 1-25, January.
    2. Mantas Dirma & Saulius Paukštys & Jonas Šiaulys, 2021. "Tails of the Moments for Sums with Dominatedly Varying Random Summands," Mathematics, MDPI, vol. 9(8), pages 1-26, April.

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